updated "op +", "op -", "op *". "HOL.divide" in src & test
find . -type f -exec sed -i s/"\"op +\""/"\"Groups.plus_class.plus\""/g {} \;
find . -type f -exec sed -i s/"\"op -\""/"\"Groups.minus_class.minus\""/g {} \;
find . -type f -exec sed -i s/"\"op *\""/"\"Groups.times_class.times\""/g {} \;
find . -type f -exec sed -i s/"\"HOL.divide\""/"\"Rings.inverse_class.divide\""/g {} \;
1 (* theory collecting all knowledge
2 (predicates 'is_rootEq_in', 'is_sqrt_in', 'is_ratEq_in')
3 for PolynomialEquations.
4 alternative dependencies see Isac.thy
10 (c) by Richard Lang, 2003
13 theory PolyEq imports LinEq RootRatEq begin
17 (*---------scripts--------------------------*)
20 bool list] => bool list"
21 ("((Script Complete'_square (_ _ =))//
26 bool list] => bool list"
27 ("((Script Normalize'_poly (_ _=))//
29 Solve'_d0'_polyeq'_equation
31 bool list] => bool list"
32 ("((Script Solve'_d0'_polyeq'_equation (_ _ =))//
34 Solve'_d1'_polyeq'_equation
36 bool list] => bool list"
37 ("((Script Solve'_d1'_polyeq'_equation (_ _ =))//
39 Solve'_d2'_polyeq'_equation
41 bool list] => bool list"
42 ("((Script Solve'_d2'_polyeq'_equation (_ _ =))//
44 Solve'_d2'_polyeq'_sqonly'_equation
46 bool list] => bool list"
47 ("((Script Solve'_d2'_polyeq'_sqonly'_equation (_ _ =))//
49 Solve'_d2'_polyeq'_bdvonly'_equation
51 bool list] => bool list"
52 ("((Script Solve'_d2'_polyeq'_bdvonly'_equation (_ _ =))//
54 Solve'_d2'_polyeq'_pq'_equation
56 bool list] => bool list"
57 ("((Script Solve'_d2'_polyeq'_pq'_equation (_ _ =))//
59 Solve'_d2'_polyeq'_abc'_equation
61 bool list] => bool list"
62 ("((Script Solve'_d2'_polyeq'_abc'_equation (_ _ =))//
64 Solve'_d3'_polyeq'_equation
66 bool list] => bool list"
67 ("((Script Solve'_d3'_polyeq'_equation (_ _ =))//
69 Solve'_d4'_polyeq'_equation
71 bool list] => bool list"
72 ("((Script Solve'_d4'_polyeq'_equation (_ _ =))//
76 bool list] => bool list"
77 ("((Script Biquadrat'_poly (_ _=))//
80 (*-------------------- rules -------------------------------------------------*)
83 cancel_leading_coeff1: "Not (c =!= 0) ==> (a + b*bdv + c*bdv^^^2 = 0) =
84 (a/c + b/c*bdv + bdv^^^2 = 0)"
85 cancel_leading_coeff2: "Not (c =!= 0) ==> (a - b*bdv + c*bdv^^^2 = 0) =
86 (a/c - b/c*bdv + bdv^^^2 = 0)"
87 cancel_leading_coeff3: "Not (c =!= 0) ==> (a + b*bdv - c*bdv^^^2 = 0) =
88 (a/c + b/c*bdv - bdv^^^2 = 0)"
90 cancel_leading_coeff4: "Not (c =!= 0) ==> (a + bdv + c*bdv^^^2 = 0) =
91 (a/c + 1/c*bdv + bdv^^^2 = 0)"
92 cancel_leading_coeff5: "Not (c =!= 0) ==> (a - bdv + c*bdv^^^2 = 0) =
93 (a/c - 1/c*bdv + bdv^^^2 = 0)"
94 cancel_leading_coeff6: "Not (c =!= 0) ==> (a + bdv - c*bdv^^^2 = 0) =
95 (a/c + 1/c*bdv - bdv^^^2 = 0)"
97 cancel_leading_coeff7: "Not (c =!= 0) ==> ( b*bdv + c*bdv^^^2 = 0) =
98 ( b/c*bdv + bdv^^^2 = 0)"
99 cancel_leading_coeff8: "Not (c =!= 0) ==> ( b*bdv - c*bdv^^^2 = 0) =
100 ( b/c*bdv - bdv^^^2 = 0)"
102 cancel_leading_coeff9: "Not (c =!= 0) ==> ( bdv + c*bdv^^^2 = 0) =
103 ( 1/c*bdv + bdv^^^2 = 0)"
104 cancel_leading_coeff10:"Not (c =!= 0) ==> ( bdv - c*bdv^^^2 = 0) =
105 ( 1/c*bdv - bdv^^^2 = 0)"
107 cancel_leading_coeff11:"Not (c =!= 0) ==> (a + b*bdv^^^2 = 0) =
109 cancel_leading_coeff12:"Not (c =!= 0) ==> (a - b*bdv^^^2 = 0) =
111 cancel_leading_coeff13:"Not (c =!= 0) ==> ( b*bdv^^^2 = 0) =
114 complete_square1: "(q + p*bdv + bdv^^^2 = 0) =
115 (q + (p/2 + bdv)^^^2 = (p/2)^^^2)"
116 complete_square2: "( p*bdv + bdv^^^2 = 0) =
117 ( (p/2 + bdv)^^^2 = (p/2)^^^2)"
118 complete_square3: "( bdv + bdv^^^2 = 0) =
119 ( (1/2 + bdv)^^^2 = (1/2)^^^2)"
121 complete_square4: "(q - p*bdv + bdv^^^2 = 0) =
122 (q + (p/2 - bdv)^^^2 = (p/2)^^^2)"
123 complete_square5: "(q + p*bdv - bdv^^^2 = 0) =
124 (q + (p/2 - bdv)^^^2 = (p/2)^^^2)"
126 square_explicit1: "(a + b^^^2 = c) = ( b^^^2 = c - a)"
127 square_explicit2: "(a - b^^^2 = c) = (-(b^^^2) = c - a)"
129 bdv_explicit1: "(a + bdv = b) = (bdv = - a + b)"
130 bdv_explicit2: "(a - bdv = b) = ((-1)*bdv = - a + b)"
131 bdv_explicit3: "((-1)*bdv = b) = (bdv = (-1)*b)"
133 plus_leq: "(0 <= a + b) = ((-1)*b <= a)"(*Isa?*)
134 minus_leq: "(0 <= a - b) = ( b <= a)"(*Isa?*)
137 (*WN0509 compare LinEq.all_left "[|Not(b=!=0)|] ==> (a=b) = (a+(-1)*b=0)"*)
138 all_left: "[|Not(b=!=0)|] ==> (a = b) = (a - b = 0)"
139 makex1_x: "a^^^1 = a"
140 real_assoc_1: "a+(b+c) = a+b+c"
141 real_assoc_2: "a*(b*c) = a*b*c"
143 (* ---- degree 0 ----*)
144 d0_true: "(0=0) = True"
145 d0_false: "[|Not(bdv occurs_in a);Not(a=0)|] ==> (a=0) = False"
146 (* ---- degree 1 ----*)
148 "[|Not(bdv occurs_in a)|] ==> (a + b*bdv = 0) = (b*bdv = (-1)*a)"
150 "[|Not(bdv occurs_in a)|] ==> (a + bdv = 0) = ( bdv = (-1)*a)"
152 "[|Not(b=0);Not(bdv occurs_in c)|] ==> (b*bdv = c) = (bdv = c/b)"
153 (* ---- degree 2 ----*)
155 "[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^2=0) = (b*bdv^^^2= (-1)*a)"
157 "[|Not(bdv occurs_in a)|] ==> (a + bdv^^^2=0) = ( bdv^^^2= (-1)*a)"
159 "[|Not(b=0);Not(bdv occurs_in c)|] ==> (b*bdv^^^2=c) = (bdv^^^2=c/b)"
161 d2_prescind1: "(a*bdv + b*bdv^^^2 = 0) = (bdv*(a +b*bdv)=0)"
162 d2_prescind2: "(a*bdv + bdv^^^2 = 0) = (bdv*(a + bdv)=0)"
163 d2_prescind3: "( bdv + b*bdv^^^2 = 0) = (bdv*(1+b*bdv)=0)"
164 d2_prescind4: "( bdv + bdv^^^2 = 0) = (bdv*(1+ bdv)=0)"
165 (* eliminate degree 2 *)
166 (* thm for neg arguments in sqroot have postfix _neg *)
167 d2_sqrt_equation1: "[|(0<=c);Not(bdv occurs_in c)|] ==>
168 (bdv^^^2=c) = ((bdv=sqrt c) | (bdv=(-1)*sqrt c ))"
169 d2_sqrt_equation1_neg:
170 "[|(c<0);Not(bdv occurs_in c)|] ==> (bdv^^^2=c) = False"
171 d2_sqrt_equation2: "(bdv^^^2=0) = (bdv=0)"
172 d2_sqrt_equation3: "(b*bdv^^^2=0) = (bdv=0)"
173 d2_reduce_equation1: "(bdv*(a +b*bdv)=0) = ((bdv=0)|(a+b*bdv=0))"
174 d2_reduce_equation2: "(bdv*(a + bdv)=0) = ((bdv=0)|(a+ bdv=0))"
175 d2_pqformula1: "[|0<=p^^^2 - 4*q|] ==> (q+p*bdv+ bdv^^^2=0) =
176 ((bdv= (-1)*(p/2) + sqrt(p^^^2 - 4*q)/2)
177 | (bdv= (-1)*(p/2) - sqrt(p^^^2 - 4*q)/2))"
178 d2_pqformula1_neg: "[|p^^^2 - 4*q<0|] ==> (q+p*bdv+ bdv^^^2=0) = False"
179 d2_pqformula2: "[|0<=p^^^2 - 4*q|] ==> (q+p*bdv+1*bdv^^^2=0) =
180 ((bdv= (-1)*(p/2) + sqrt(p^^^2 - 4*q)/2)
181 | (bdv= (-1)*(p/2) - sqrt(p^^^2 - 4*q)/2))"
182 d2_pqformula2_neg: "[|p^^^2 - 4*q<0|] ==> (q+p*bdv+1*bdv^^^2=0) = False"
183 d2_pqformula3: "[|0<=1 - 4*q|] ==> (q+ bdv+ bdv^^^2=0) =
184 ((bdv= (-1)*(1/2) + sqrt(1 - 4*q)/2)
185 | (bdv= (-1)*(1/2) - sqrt(1 - 4*q)/2))"
186 d2_pqformula3_neg: "[|1 - 4*q<0|] ==> (q+ bdv+ bdv^^^2=0) = False"
187 d2_pqformula4: "[|0<=1 - 4*q|] ==> (q+ bdv+1*bdv^^^2=0) =
188 ((bdv= (-1)*(1/2) + sqrt(1 - 4*q)/2)
189 | (bdv= (-1)*(1/2) - sqrt(1 - 4*q)/2))"
190 d2_pqformula4_neg: "[|1 - 4*q<0|] ==> (q+ bdv+1*bdv^^^2=0) = False"
191 d2_pqformula5: "[|0<=p^^^2 - 0|] ==> ( p*bdv+ bdv^^^2=0) =
192 ((bdv= (-1)*(p/2) + sqrt(p^^^2 - 0)/2)
193 | (bdv= (-1)*(p/2) - sqrt(p^^^2 - 0)/2))"
194 (* d2_pqformula5_neg not need p^2 never less zero in R *)
195 d2_pqformula6: "[|0<=p^^^2 - 0|] ==> ( p*bdv+1*bdv^^^2=0) =
196 ((bdv= (-1)*(p/2) + sqrt(p^^^2 - 0)/2)
197 | (bdv= (-1)*(p/2) - sqrt(p^^^2 - 0)/2))"
198 (* d2_pqformula6_neg not need p^2 never less zero in R *)
199 d2_pqformula7: "[|0<=1 - 0|] ==> ( bdv+ bdv^^^2=0) =
200 ((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
201 | (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))"
202 (* d2_pqformula7_neg not need, because 1<0 ==> False*)
203 d2_pqformula8: "[|0<=1 - 0|] ==> ( bdv+1*bdv^^^2=0) =
204 ((bdv= (-1)*(1/2) + sqrt(1 - 0)/2)
205 | (bdv= (-1)*(1/2) - sqrt(1 - 0)/2))"
206 (* d2_pqformula8_neg not need, because 1<0 ==> False*)
207 d2_pqformula9: "[|Not(bdv occurs_in q); 0<= (-1)*4*q|] ==>
208 (q+ 1*bdv^^^2=0) = ((bdv= 0 + sqrt(0 - 4*q)/2)
209 | (bdv= 0 - sqrt(0 - 4*q)/2))"
211 "[|Not(bdv occurs_in q); (-1)*4*q<0|] ==> (q+ 1*bdv^^^2=0) = False"
213 "[|Not(bdv occurs_in q); 0<= (-1)*4*q|] ==> (q+ bdv^^^2=0) =
214 ((bdv= 0 + sqrt(0 - 4*q)/2)
215 | (bdv= 0 - sqrt(0 - 4*q)/2))"
217 "[|Not(bdv occurs_in q); (-1)*4*q<0|] ==> (q+ bdv^^^2=0) = False"
219 "[|0<=b^^^2 - 4*a*c|] ==> (c + b*bdv+a*bdv^^^2=0) =
220 ((bdv=( -b + sqrt(b^^^2 - 4*a*c))/(2*a))
221 | (bdv=( -b - sqrt(b^^^2 - 4*a*c))/(2*a)))"
223 "[|b^^^2 - 4*a*c<0|] ==> (c + b*bdv+a*bdv^^^2=0) = False"
225 "[|0<=1 - 4*a*c|] ==> (c+ bdv+a*bdv^^^2=0) =
226 ((bdv=( -1 + sqrt(1 - 4*a*c))/(2*a))
227 | (bdv=( -1 - sqrt(1 - 4*a*c))/(2*a)))"
229 "[|1 - 4*a*c<0|] ==> (c+ bdv+a*bdv^^^2=0) = False"
231 "[|0<=b^^^2 - 4*1*c|] ==> (c + b*bdv+ bdv^^^2=0) =
232 ((bdv=( -b + sqrt(b^^^2 - 4*1*c))/(2*1))
233 | (bdv=( -b - sqrt(b^^^2 - 4*1*c))/(2*1)))"
235 "[|b^^^2 - 4*1*c<0|] ==> (c + b*bdv+ bdv^^^2=0) = False"
237 "[|0<=1 - 4*1*c|] ==> (c + bdv+ bdv^^^2=0) =
238 ((bdv=( -1 + sqrt(1 - 4*1*c))/(2*1))
239 | (bdv=( -1 - sqrt(1 - 4*1*c))/(2*1)))"
241 "[|1 - 4*1*c<0|] ==> (c + bdv+ bdv^^^2=0) = False"
243 "[|Not(bdv occurs_in c); 0<=0 - 4*a*c|] ==> (c + a*bdv^^^2=0) =
244 ((bdv=( 0 + sqrt(0 - 4*a*c))/(2*a))
245 | (bdv=( 0 - sqrt(0 - 4*a*c))/(2*a)))"
247 "[|Not(bdv occurs_in c); 0 - 4*a*c<0|] ==> (c + a*bdv^^^2=0) = False"
249 "[|Not(bdv occurs_in c); 0<=0 - 4*1*c|] ==> (c+ bdv^^^2=0) =
250 ((bdv=( 0 + sqrt(0 - 4*1*c))/(2*1))
251 | (bdv=( 0 - sqrt(0 - 4*1*c))/(2*1)))"
253 "[|Not(bdv occurs_in c); 0 - 4*1*c<0|] ==> (c+ bdv^^^2=0) = False"
255 "[|0<=b^^^2 - 0|] ==> ( b*bdv+a*bdv^^^2=0) =
256 ((bdv=( -b + sqrt(b^^^2 - 0))/(2*a))
257 | (bdv=( -b - sqrt(b^^^2 - 0))/(2*a)))"
258 (* d2_abcformula7_neg not need b^2 never less zero in R *)
260 "[|0<=b^^^2 - 0|] ==> ( b*bdv+ bdv^^^2=0) =
261 ((bdv=( -b + sqrt(b^^^2 - 0))/(2*1))
262 | (bdv=( -b - sqrt(b^^^2 - 0))/(2*1)))"
263 (* d2_abcformula8_neg not need b^2 never less zero in R *)
265 "[|0<=1 - 0|] ==> ( bdv+a*bdv^^^2=0) =
266 ((bdv=( -1 + sqrt(1 - 0))/(2*a))
267 | (bdv=( -1 - sqrt(1 - 0))/(2*a)))"
268 (* d2_abcformula9_neg not need, because 1<0 ==> False*)
270 "[|0<=1 - 0|] ==> ( bdv+ bdv^^^2=0) =
271 ((bdv=( -1 + sqrt(1 - 0))/(2*1))
272 | (bdv=( -1 - sqrt(1 - 0))/(2*1)))"
273 (* d2_abcformula10_neg not need, because 1<0 ==> False*)
275 (* ---- degree 3 ----*)
277 "(a*bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a + b*bdv + c*bdv^^^2=0))"
279 "( bdv + b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 + b*bdv + c*bdv^^^2=0))"
281 "(a*bdv + bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (a + bdv + c*bdv^^^2=0))"
283 "( bdv + bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | (1 + bdv + c*bdv^^^2=0))"
285 "(a*bdv + b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | (a + b*bdv + bdv^^^2=0))"
287 "( bdv + b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + b*bdv + bdv^^^2=0))"
289 "(a*bdv + bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + bdv + bdv^^^2=0))"
291 "( bdv + bdv^^^2 + bdv^^^3=0) = (bdv=0 | (1 + bdv + bdv^^^2=0))"
293 "(a*bdv + c*bdv^^^3=0) = (bdv=0 | (a + c*bdv^^^2=0))"
294 d3_reduce_equation10:
295 "( bdv + c*bdv^^^3=0) = (bdv=0 | (1 + c*bdv^^^2=0))"
296 d3_reduce_equation11:
297 "(a*bdv + bdv^^^3=0) = (bdv=0 | (a + bdv^^^2=0))"
298 d3_reduce_equation12:
299 "( bdv + bdv^^^3=0) = (bdv=0 | (1 + bdv^^^2=0))"
300 d3_reduce_equation13:
301 "( b*bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | ( b*bdv + c*bdv^^^2=0))"
302 d3_reduce_equation14:
303 "( bdv^^^2 + c*bdv^^^3=0) = (bdv=0 | ( bdv + c*bdv^^^2=0))"
304 d3_reduce_equation15:
305 "( b*bdv^^^2 + bdv^^^3=0) = (bdv=0 | ( b*bdv + bdv^^^2=0))"
306 d3_reduce_equation16:
307 "( bdv^^^2 + bdv^^^3=0) = (bdv=0 | ( bdv + bdv^^^2=0))"
309 "[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^3=0) = (b*bdv^^^3= (-1)*a)"
311 "[|Not(bdv occurs_in a)|] ==> (a + bdv^^^3=0) = ( bdv^^^3= (-1)*a)"
313 "[|Not(b=0);Not(bdv occurs_in a)|] ==> (b*bdv^^^3=c) = (bdv^^^3=c/b)"
315 "(bdv^^^3=0) = (bdv=0)"
317 "(bdv^^^3=c) = (bdv = nroot 3 c)"
319 (* ---- degree 4 ----*)
320 (* RL03.FIXME es wir nicht getestet ob u>0 *)
322 "(c+b*bdv^^^2+a*bdv^^^4=0) =
323 ((a*u^^^2+b*u+c=0) & (bdv^^^2=u))"
325 (* ---- 7.3.02 von Termorder ---- *)
327 bdv_collect_1: "l * bdv + m * bdv = (l + m) * bdv"
328 bdv_collect_2: "bdv + m * bdv = (1 + m) * bdv"
329 bdv_collect_3: "l * bdv + bdv = (l + 1) * bdv"
331 (* bdv_collect_assoc0_1 "l * bdv + m * bdv + k = (l + m) * bdv + k"
332 bdv_collect_assoc0_2 "bdv + m * bdv + k = (1 + m) * bdv + k"
333 bdv_collect_assoc0_3 "l * bdv + bdv + k = (l + 1) * bdv + k"
335 bdv_collect_assoc1_1:"l * bdv + (m * bdv + k) = (l + m) * bdv + k"
336 bdv_collect_assoc1_2:"bdv + (m * bdv + k) = (1 + m) * bdv + k"
337 bdv_collect_assoc1_3:"l * bdv + (bdv + k) = (l + 1) * bdv + k"
339 bdv_collect_assoc2_1:"k + l * bdv + m * bdv = k + (l + m) * bdv"
340 bdv_collect_assoc2_2:"k + bdv + m * bdv = k + (1 + m) * bdv"
341 bdv_collect_assoc2_3:"k + l * bdv + bdv = k + (l + 1) * bdv"
344 bdv_n_collect_1: "l * bdv^^^n + m * bdv^^^n = (l + m) * bdv^^^n"
345 bdv_n_collect_2: " bdv^^^n + m * bdv^^^n = (1 + m) * bdv^^^n"
346 bdv_n_collect_3: "l * bdv^^^n + bdv^^^n = (l + 1) * bdv^^^n" (*order!*)
348 bdv_n_collect_assoc1_1:"l * bdv^^^n + (m * bdv^^^n + k) = (l + m) * bdv^^^n + k"
349 bdv_n_collect_assoc1_2:"bdv^^^n + (m * bdv^^^n + k) = (1 + m) * bdv^^^n + k"
350 bdv_n_collect_assoc1_3:"l * bdv^^^n + (bdv^^^n + k) = (l + 1) * bdv^^^n + k"
352 bdv_n_collect_assoc2_1:"k + l * bdv^^^n + m * bdv^^^n = k + (l + m) * bdv^^^n"
353 bdv_n_collect_assoc2_2:"k + bdv^^^n + m * bdv^^^n = k + (1 + m) * bdv^^^n"
354 bdv_n_collect_assoc2_3:"k + l * bdv^^^n + bdv^^^n = k + (l + 1) * bdv^^^n"
357 real_minus_div: "- (a / b) = (-1 * a) / b"
359 separate_bdv: "(a * bdv) / b = (a / b) * bdv"
360 separate_bdv_n: "(a * bdv ^^^ n) / b = (a / b) * bdv ^^^ n"
361 separate_1_bdv: "bdv / b = (1 / b) * bdv"
362 separate_1_bdv_n: "bdv ^^^ n / b = (1 / b) * bdv ^^^ n"
367 (*-------------------------rulse-------------------------*)
368 val PolyEq_prls = (*3.10.02:just the following order due to subterm evaluation*)
369 append_rls "PolyEq_prls" e_rls
370 [Calc ("Atools.ident",eval_ident "#ident_"),
371 Calc ("Tools.matches",eval_matches ""),
372 Calc ("Tools.lhs" ,eval_lhs ""),
373 Calc ("Tools.rhs" ,eval_rhs ""),
374 Calc ("Poly.is'_expanded'_in",eval_is_expanded_in ""),
375 Calc ("Poly.is'_poly'_in",eval_is_poly_in ""),
376 Calc ("Poly.has'_degree'_in",eval_has_degree_in ""),
377 Calc ("Poly.is'_polyrat'_in",eval_is_polyrat_in ""),
378 (*Calc ("Atools.occurs'_in",eval_occurs_in ""), *)
379 (*Calc ("Atools.is'_const",eval_const "#is_const_"),*)
380 Calc ("op =",eval_equal "#equal_"),
381 Calc ("RootEq.is'_rootTerm'_in",eval_is_rootTerm_in ""),
382 Calc ("RatEq.is'_ratequation'_in",eval_is_ratequation_in ""),
383 Thm ("not_true",num_str @{thm not_true}),
384 Thm ("not_false",num_str @{thm not_false}),
385 Thm ("and_true",num_str @{thm and_true}),
386 Thm ("and_false",num_str @{thm and_false}),
387 Thm ("or_true",num_str @{thm or_true}),
388 Thm ("or_false",num_str @{thm or_false})
392 merge_rls "PolyEq_erls" LinEq_erls
393 (append_rls "ops_preds" calculate_Rational
394 [Calc ("op =",eval_equal "#equal_"),
395 Thm ("plus_leq", num_str @{thm plus_leq}),
396 Thm ("minus_leq", num_str @{thm minus_leq}),
397 Thm ("rat_leq1", num_str @{thm rat_leq1}),
398 Thm ("rat_leq2", num_str @{thm rat_leq2}),
399 Thm ("rat_leq3", num_str @{thm rat_leq3})
403 merge_rls "PolyEq_crls" LinEq_crls
404 (append_rls "ops_preds" calculate_Rational
405 [Calc ("op =",eval_equal "#equal_"),
406 Thm ("plus_leq", num_str @{thm plus_leq}),
407 Thm ("minus_leq", num_str @{thm minus_leq}),
408 Thm ("rat_leq1", num_str @{thm rat_leq1}),
409 Thm ("rat_leq2", num_str @{thm rat_leq2}),
410 Thm ("rat_leq3", num_str @{thm rat_leq3})
413 val cancel_leading_coeff = prep_rls(
414 Rls {id = "cancel_leading_coeff", preconds = [],
415 rew_ord = ("e_rew_ord",e_rew_ord),
416 erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
418 [Thm ("cancel_leading_coeff1",num_str @{thm cancel_leading_coeff1}),
419 Thm ("cancel_leading_coeff2",num_str @{thm cancel_leading_coeff2}),
420 Thm ("cancel_leading_coeff3",num_str @{thm cancel_leading_coeff3}),
421 Thm ("cancel_leading_coeff4",num_str @{thm cancel_leading_coeff4}),
422 Thm ("cancel_leading_coeff5",num_str @{thm cancel_leading_coeff5}),
423 Thm ("cancel_leading_coeff6",num_str @{thm cancel_leading_coeff6}),
424 Thm ("cancel_leading_coeff7",num_str @{thm cancel_leading_coeff7}),
425 Thm ("cancel_leading_coeff8",num_str @{thm cancel_leading_coeff8}),
426 Thm ("cancel_leading_coeff9",num_str @{thm cancel_leading_coeff9}),
427 Thm ("cancel_leading_coeff10",num_str @{thm cancel_leading_coeff10}),
428 Thm ("cancel_leading_coeff11",num_str @{thm cancel_leading_coeff11}),
429 Thm ("cancel_leading_coeff12",num_str @{thm cancel_leading_coeff12}),
430 Thm ("cancel_leading_coeff13",num_str @{thm cancel_leading_coeff13})
431 ],scr = Script ((term_of o the o (parse thy)) "empty_script")}:rls);
434 val complete_square = prep_rls(
435 Rls {id = "complete_square", preconds = [],
436 rew_ord = ("e_rew_ord",e_rew_ord),
437 erls = PolyEq_erls, srls = Erls, calc = [], (*asm_thm = [],*)
438 rules = [Thm ("complete_square1",num_str @{thm complete_square1}),
439 Thm ("complete_square2",num_str @{thm complete_square2}),
440 Thm ("complete_square3",num_str @{thm complete_square3}),
441 Thm ("complete_square4",num_str @{thm complete_square4}),
442 Thm ("complete_square5",num_str @{thm complete_square5})
444 scr = Script ((term_of o the o (parse thy))
448 val polyeq_simplify = prep_rls(
449 Rls {id = "polyeq_simplify", preconds = [],
450 rew_ord = ("termlessI",termlessI),
455 rules = [Thm ("real_assoc_1",num_str @{thm real_assoc_1}),
456 Thm ("real_assoc_2",num_str @{thm real_assoc_2}),
457 Thm ("real_diff_minus",num_str @{thm real_diff_minus}),
458 Thm ("real_unari_minus",num_str @{thm real_unari_minus}),
459 Thm ("realpow_multI",num_str @{thm realpow_multI}),
460 Calc ("Groups.plus_class.plus",eval_binop "#add_"),
461 Calc ("Groups.minus_class.minus",eval_binop "#sub_"),
462 Calc ("op *",eval_binop "#mult_"),
463 Calc ("Rings.inverse_class.divide", eval_cancel "#divide_e"),
464 Calc ("NthRoot.sqrt",eval_sqrt "#sqrt_"),
465 Calc ("Atools.pow" ,eval_binop "#power_"),
468 scr = Script ((term_of o the o (parse thy)) "empty_script")
471 ruleset' := overwritelthy @{theory} (!ruleset',
472 [("cancel_leading_coeff",cancel_leading_coeff),
473 ("complete_square",complete_square),
474 ("PolyEq_erls",PolyEq_erls),(*FIXXXME:del with rls.rls'*)
475 ("polyeq_simplify",polyeq_simplify)]);
480 (* ------------- polySolve ------------------ *)
482 (*isolate the bound variable in an d0 equation; 'bdv' is a meta-constant*)
483 val d0_polyeq_simplify = prep_rls(
484 Rls {id = "d0_polyeq_simplify", preconds = [],
485 rew_ord = ("e_rew_ord",e_rew_ord),
490 rules = [Thm("d0_true",num_str @{thm d0_true}),
491 Thm("d0_false",num_str @{thm d0_false})
493 scr = Script ((term_of o the o (parse thy)) "empty_script")
497 (*isolate the bound variable in an d1 equation; 'bdv' is a meta-constant*)
498 val d1_polyeq_simplify = prep_rls(
499 Rls {id = "d1_polyeq_simplify", preconds = [],
500 rew_ord = ("e_rew_ord",e_rew_ord),
504 (*asm_thm = [("d1_isolate_div","")],*)
506 Thm("d1_isolate_add1",num_str @{thm d1_isolate_add1}),
507 (* a+bx=0 -> bx=-a *)
508 Thm("d1_isolate_add2",num_str @{thm d1_isolate_add2}),
510 Thm("d1_isolate_div",num_str @{thm d1_isolate_div})
513 scr = Script ((term_of o the o (parse thy)) "empty_script")
519 (* isolate the bound variable in an d2 equation with bdv only;
520 'bdv' is a meta-constant*)
521 val d2_polyeq_bdv_only_simplify = prep_rls(
522 Rls {id = "d2_polyeq_bdv_only_simplify", preconds = [],
523 rew_ord = ("e_rew_ord",e_rew_ord),
527 (*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
528 ("d2_isolate_div","")],*)
529 rules = [Thm("d2_prescind1",num_str @{thm d2_prescind1}),
530 (* ax+bx^2=0 -> x(a+bx)=0 *)
531 Thm("d2_prescind2",num_str @{thm d2_prescind2}),
532 (* ax+ x^2=0 -> x(a+ x)=0 *)
533 Thm("d2_prescind3",num_str @{thm d2_prescind3}),
534 (* x+bx^2=0 -> x(1+bx)=0 *)
535 Thm("d2_prescind4",num_str @{thm d2_prescind4}),
536 (* x+ x^2=0 -> x(1+ x)=0 *)
537 Thm("d2_sqrt_equation1",num_str @{thm d2_sqrt_equation1}),
538 (* x^2=c -> x=+-sqrt(c)*)
539 Thm("d2_sqrt_equation1_neg",num_str @{thm d2_sqrt_equation1_neg}),
540 (* [0<c] x^2=c -> [] *)
541 Thm("d2_sqrt_equation2",num_str @{thm d2_sqrt_equation2}),
543 Thm("d2_reduce_equation1",num_str @{thm d2_reduce_equation1}),
544 (* x(a+bx)=0 -> x=0 | a+bx=0*)
545 Thm("d2_reduce_equation2",num_str @{thm d2_reduce_equation2}),
546 (* x(a+ x)=0 -> x=0 | a+ x=0*)
547 Thm("d2_isolate_div",num_str @{thm d2_isolate_div})
548 (* bx^2=c -> x^2=c/b*)
550 scr = Script ((term_of o the o (parse thy)) "empty_script")
554 (* isolate the bound variable in an d2 equation with sqrt only;
555 'bdv' is a meta-constant*)
556 val d2_polyeq_sq_only_simplify = prep_rls(
557 Rls {id = "d2_polyeq_sq_only_simplify", preconds = [],
558 rew_ord = ("e_rew_ord",e_rew_ord),
562 (*asm_thm = [("d2_sqrt_equation1",""),("d2_sqrt_equation1_neg",""),
563 ("d2_isolate_div","")],*)
564 rules = [Thm("d2_isolate_add1",num_str @{thm d2_isolate_add1}),
565 (* a+ bx^2=0 -> bx^2=(-1)a*)
566 Thm("d2_isolate_add2",num_str @{thm d2_isolate_add2}),
567 (* a+ x^2=0 -> x^2=(-1)a*)
568 Thm("d2_sqrt_equation2",num_str @{thm d2_sqrt_equation2}),
570 Thm("d2_sqrt_equation1",num_str @{thm d2_sqrt_equation1}),
571 (* x^2=c -> x=+-sqrt(c)*)
572 Thm("d2_sqrt_equation1_neg",num_str @{thm d2_sqrt_equation1_neg}),
573 (* [c<0] x^2=c -> x=[] *)
574 Thm("d2_isolate_div",num_str @{thm d2_isolate_div})
575 (* bx^2=c -> x^2=c/b*)
577 scr = Script ((term_of o the o (parse thy)) "empty_script")
581 (* isolate the bound variable in an d2 equation with pqFormula;
582 'bdv' is a meta-constant*)
583 val d2_polyeq_pqFormula_simplify = prep_rls(
584 Rls {id = "d2_polyeq_pqFormula_simplify", preconds = [],
585 rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
586 srls = Erls, calc = [],
587 rules = [Thm("d2_pqformula1",num_str @{thm d2_pqformula1}),
589 Thm("d2_pqformula1_neg",num_str @{thm d2_pqformula1_neg}),
591 Thm("d2_pqformula2",num_str @{thm d2_pqformula2}),
593 Thm("d2_pqformula2_neg",num_str @{thm d2_pqformula2_neg}),
595 Thm("d2_pqformula3",num_str @{thm d2_pqformula3}),
597 Thm("d2_pqformula3_neg",num_str @{thm d2_pqformula3_neg}),
599 Thm("d2_pqformula4",num_str @{thm d2_pqformula4}),
601 Thm("d2_pqformula4_neg",num_str @{thm d2_pqformula4_neg}),
603 Thm("d2_pqformula5",num_str @{thm d2_pqformula5}),
605 Thm("d2_pqformula6",num_str @{thm d2_pqformula6}),
607 Thm("d2_pqformula7",num_str @{thm d2_pqformula7}),
609 Thm("d2_pqformula8",num_str @{thm d2_pqformula8}),
611 Thm("d2_pqformula9",num_str @{thm d2_pqformula9}),
613 Thm("d2_pqformula9_neg",num_str @{thm d2_pqformula9_neg}),
615 Thm("d2_pqformula10",num_str @{thm d2_pqformula10}),
617 Thm("d2_pqformula10_neg",num_str @{thm d2_pqformula10_neg}),
619 Thm("d2_sqrt_equation2",num_str @{thm d2_sqrt_equation2}),
621 Thm("d2_sqrt_equation3",num_str @{thm d2_sqrt_equation3})
623 ],scr = Script ((term_of o the o (parse thy)) "empty_script")
627 (* isolate the bound variable in an d2 equation with abcFormula;
628 'bdv' is a meta-constant*)
629 val d2_polyeq_abcFormula_simplify = prep_rls(
630 Rls {id = "d2_polyeq_abcFormula_simplify", preconds = [],
631 rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
632 srls = Erls, calc = [],
633 rules = [Thm("d2_abcformula1",num_str @{thm d2_abcformula1}),
635 Thm("d2_abcformula1_neg",num_str @{thm d2_abcformula1_neg}),
637 Thm("d2_abcformula2",num_str @{thm d2_abcformula2}),
639 Thm("d2_abcformula2_neg",num_str @{thm d2_abcformula2_neg}),
641 Thm("d2_abcformula3",num_str @{thm d2_abcformula3}),
643 Thm("d2_abcformula3_neg",num_str @{thm d2_abcformula3_neg}),
645 Thm("d2_abcformula4",num_str @{thm d2_abcformula4}),
647 Thm("d2_abcformula4_neg",num_str @{thm d2_abcformula4_neg}),
649 Thm("d2_abcformula5",num_str @{thm d2_abcformula5}),
651 Thm("d2_abcformula5_neg",num_str @{thm d2_abcformula5_neg}),
653 Thm("d2_abcformula6",num_str @{thm d2_abcformula6}),
655 Thm("d2_abcformula6_neg",num_str @{thm d2_abcformula6_neg}),
657 Thm("d2_abcformula7",num_str @{thm d2_abcformula7}),
659 Thm("d2_abcformula8",num_str @{thm d2_abcformula8}),
661 Thm("d2_abcformula9",num_str @{thm d2_abcformula9}),
663 Thm("d2_abcformula10",num_str @{thm d2_abcformula10}),
665 Thm("d2_sqrt_equation2",num_str @{thm d2_sqrt_equation2}),
667 Thm("d2_sqrt_equation3",num_str @{thm d2_sqrt_equation3})
670 scr = Script ((term_of o the o (parse thy)) "empty_script")
675 (* isolate the bound variable in an d2 equation;
676 'bdv' is a meta-constant*)
677 val d2_polyeq_simplify = prep_rls(
678 Rls {id = "d2_polyeq_simplify", preconds = [],
679 rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
680 srls = Erls, calc = [],
681 rules = [Thm("d2_pqformula1",num_str @{thm d2_pqformula1}),
683 Thm("d2_pqformula1_neg",num_str @{thm d2_pqformula1_neg}),
685 Thm("d2_pqformula2",num_str @{thm d2_pqformula2}),
687 Thm("d2_pqformula2_neg",num_str @{thm d2_pqformula2_neg}),
689 Thm("d2_pqformula3",num_str @{thm d2_pqformula3}),
691 Thm("d2_pqformula3_neg",num_str @{thm d2_pqformula3_neg}),
693 Thm("d2_pqformula4",num_str @{thm d2_pqformula4}),
695 Thm("d2_pqformula4_neg",num_str @{thm d2_pqformula4_neg}),
697 Thm("d2_abcformula1",num_str @{thm d2_abcformula1}),
699 Thm("d2_abcformula1_neg",num_str @{thm d2_abcformula1_neg}),
701 Thm("d2_abcformula2",num_str @{thm d2_abcformula2}),
703 Thm("d2_abcformula2_neg",num_str @{thm d2_abcformula2_neg}),
705 Thm("d2_prescind1",num_str @{thm d2_prescind1}),
706 (* ax+bx^2=0 -> x(a+bx)=0 *)
707 Thm("d2_prescind2",num_str @{thm d2_prescind2}),
708 (* ax+ x^2=0 -> x(a+ x)=0 *)
709 Thm("d2_prescind3",num_str @{thm d2_prescind3}),
710 (* x+bx^2=0 -> x(1+bx)=0 *)
711 Thm("d2_prescind4",num_str @{thm d2_prescind4}),
712 (* x+ x^2=0 -> x(1+ x)=0 *)
713 Thm("d2_isolate_add1",num_str @{thm d2_isolate_add1}),
714 (* a+ bx^2=0 -> bx^2=(-1)a*)
715 Thm("d2_isolate_add2",num_str @{thm d2_isolate_add2}),
716 (* a+ x^2=0 -> x^2=(-1)a*)
717 Thm("d2_sqrt_equation1",num_str @{thm d2_sqrt_equation1}),
718 (* x^2=c -> x=+-sqrt(c)*)
719 Thm("d2_sqrt_equation1_neg",num_str @{thm d2_sqrt_equation1_neg}),
720 (* [c<0] x^2=c -> x=[]*)
721 Thm("d2_sqrt_equation2",num_str @{thm d2_sqrt_equation2}),
723 Thm("d2_reduce_equation1",num_str @{thm d2_reduce_equation1}),
724 (* x(a+bx)=0 -> x=0 | a+bx=0*)
725 Thm("d2_reduce_equation2",num_str @{thm d2_reduce_equation2}),
726 (* x(a+ x)=0 -> x=0 | a+ x=0*)
727 Thm("d2_isolate_div",num_str @{thm d2_isolate_div})
728 (* bx^2=c -> x^2=c/b*)
730 scr = Script ((term_of o the o (parse thy)) "empty_script")
736 (* isolate the bound variable in an d3 equation; 'bdv' is a meta-constant *)
737 val d3_polyeq_simplify = prep_rls(
738 Rls {id = "d3_polyeq_simplify", preconds = [],
739 rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
740 srls = Erls, calc = [],
742 [Thm("d3_reduce_equation1",num_str @{thm d3_reduce_equation1}),
743 (*a*bdv + b*bdv^^^2 + c*bdv^^^3=0) =
744 (bdv=0 | (a + b*bdv + c*bdv^^^2=0)*)
745 Thm("d3_reduce_equation2",num_str @{thm d3_reduce_equation2}),
746 (* bdv + b*bdv^^^2 + c*bdv^^^3=0) =
747 (bdv=0 | (1 + b*bdv + c*bdv^^^2=0)*)
748 Thm("d3_reduce_equation3",num_str @{thm d3_reduce_equation3}),
749 (*a*bdv + bdv^^^2 + c*bdv^^^3=0) =
750 (bdv=0 | (a + bdv + c*bdv^^^2=0)*)
751 Thm("d3_reduce_equation4",num_str @{thm d3_reduce_equation4}),
752 (* bdv + bdv^^^2 + c*bdv^^^3=0) =
753 (bdv=0 | (1 + bdv + c*bdv^^^2=0)*)
754 Thm("d3_reduce_equation5",num_str @{thm d3_reduce_equation5}),
755 (*a*bdv + b*bdv^^^2 + bdv^^^3=0) =
756 (bdv=0 | (a + b*bdv + bdv^^^2=0)*)
757 Thm("d3_reduce_equation6",num_str @{thm d3_reduce_equation6}),
758 (* bdv + b*bdv^^^2 + bdv^^^3=0) =
759 (bdv=0 | (1 + b*bdv + bdv^^^2=0)*)
760 Thm("d3_reduce_equation7",num_str @{thm d3_reduce_equation7}),
761 (*a*bdv + bdv^^^2 + bdv^^^3=0) =
762 (bdv=0 | (1 + bdv + bdv^^^2=0)*)
763 Thm("d3_reduce_equation8",num_str @{thm d3_reduce_equation8}),
764 (* bdv + bdv^^^2 + bdv^^^3=0) =
765 (bdv=0 | (1 + bdv + bdv^^^2=0)*)
766 Thm("d3_reduce_equation9",num_str @{thm d3_reduce_equation9}),
767 (*a*bdv + c*bdv^^^3=0) =
768 (bdv=0 | (a + c*bdv^^^2=0)*)
769 Thm("d3_reduce_equation10",num_str @{thm d3_reduce_equation10}),
770 (* bdv + c*bdv^^^3=0) =
771 (bdv=0 | (1 + c*bdv^^^2=0)*)
772 Thm("d3_reduce_equation11",num_str @{thm d3_reduce_equation11}),
773 (*a*bdv + bdv^^^3=0) =
774 (bdv=0 | (a + bdv^^^2=0)*)
775 Thm("d3_reduce_equation12",num_str @{thm d3_reduce_equation12}),
776 (* bdv + bdv^^^3=0) =
777 (bdv=0 | (1 + bdv^^^2=0)*)
778 Thm("d3_reduce_equation13",num_str @{thm d3_reduce_equation13}),
779 (* b*bdv^^^2 + c*bdv^^^3=0) =
780 (bdv=0 | ( b*bdv + c*bdv^^^2=0)*)
781 Thm("d3_reduce_equation14",num_str @{thm d3_reduce_equation14}),
782 (* bdv^^^2 + c*bdv^^^3=0) =
783 (bdv=0 | ( bdv + c*bdv^^^2=0)*)
784 Thm("d3_reduce_equation15",num_str @{thm d3_reduce_equation15}),
785 (* b*bdv^^^2 + bdv^^^3=0) =
786 (bdv=0 | ( b*bdv + bdv^^^2=0)*)
787 Thm("d3_reduce_equation16",num_str @{thm d3_reduce_equation16}),
788 (* bdv^^^2 + bdv^^^3=0) =
789 (bdv=0 | ( bdv + bdv^^^2=0)*)
790 Thm("d3_isolate_add1",num_str @{thm d3_isolate_add1}),
791 (*[|Not(bdv occurs_in a)|] ==> (a + b*bdv^^^3=0) =
792 (bdv=0 | (b*bdv^^^3=a)*)
793 Thm("d3_isolate_add2",num_str @{thm d3_isolate_add2}),
794 (*[|Not(bdv occurs_in a)|] ==> (a + bdv^^^3=0) =
795 (bdv=0 | ( bdv^^^3=a)*)
796 Thm("d3_isolate_div",num_str @{thm d3_isolate_div}),
797 (*[|Not(b=0)|] ==> (b*bdv^^^3=c) = (bdv^^^3=c/b*)
798 Thm("d3_root_equation2",num_str @{thm d3_root_equation2}),
799 (*(bdv^^^3=0) = (bdv=0) *)
800 Thm("d3_root_equation1",num_str @{thm d3_root_equation1})
801 (*bdv^^^3=c) = (bdv = nroot 3 c*)
803 scr = Script ((term_of o the o (parse thy)) "empty_script")
809 (*isolate the bound variable in an d4 equation; 'bdv' is a meta-constant*)
810 val d4_polyeq_simplify = prep_rls(
811 Rls {id = "d4_polyeq_simplify", preconds = [],
812 rew_ord = ("e_rew_ord",e_rew_ord), erls = PolyEq_erls,
813 srls = Erls, calc = [],
815 [Thm("d4_sub_u1",num_str @{thm d4_sub_u1})
816 (* ax^4+bx^2+c=0 -> x=+-sqrt(ax^2+bx^+c) *)
818 scr = Script ((term_of o the o (parse thy)) "empty_script")
822 overwritelthy @{theory}
824 [("d0_polyeq_simplify", d0_polyeq_simplify),
825 ("d1_polyeq_simplify", d1_polyeq_simplify),
826 ("d2_polyeq_simplify", d2_polyeq_simplify),
827 ("d2_polyeq_bdv_only_simplify", d2_polyeq_bdv_only_simplify),
828 ("d2_polyeq_sq_only_simplify", d2_polyeq_sq_only_simplify),
829 ("d2_polyeq_pqFormula_simplify", d2_polyeq_pqFormula_simplify),
830 ("d2_polyeq_abcFormula_simplify",
831 d2_polyeq_abcFormula_simplify),
832 ("d3_polyeq_simplify", d3_polyeq_simplify),
833 ("d4_polyeq_simplify", d4_polyeq_simplify)
838 (*------------------------problems------------------------*)
840 (get_pbt ["degree_2","polynomial","univariate","equation"]);
844 (*-------------------------poly-----------------------*)
846 (prep_pbt thy "pbl_equ_univ_poly" [] e_pblID
847 (["polynomial","univariate","equation"],
848 [("#Given" ,["equality e_e","solveFor v_v"]),
849 ("#Where" ,["~((e_e::bool) is_ratequation_in (v_v::real))",
850 "~((lhs e_e) is_rootTerm_in (v_v::real))",
851 "~((rhs e_e) is_rootTerm_in (v_v::real))"]),
852 ("#Find" ,["solutions v_v'i'"])
854 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
858 (prep_pbt thy "pbl_equ_univ_poly_deg0" [] e_pblID
859 (["degree_0","polynomial","univariate","equation"],
860 [("#Given" ,["equality e_e","solveFor v_v"]),
861 ("#Where" ,["matches (?a = 0) e_e",
862 "(lhs e_e) is_poly_in v_v",
863 "((lhs e_e) has_degree_in v_v ) = 0"
865 ("#Find" ,["solutions v_v'i'"])
867 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
868 [["PolyEq","solve_d0_polyeq_equation"]]));
872 (prep_pbt thy "pbl_equ_univ_poly_deg1" [] e_pblID
873 (["degree_1","polynomial","univariate","equation"],
874 [("#Given" ,["equality e_e","solveFor v_v"]),
875 ("#Where" ,["matches (?a = 0) e_e",
876 "(lhs e_e) is_poly_in v_v",
877 "((lhs e_e) has_degree_in v_v ) = 1"
879 ("#Find" ,["solutions v_v'i'"])
881 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
882 [["PolyEq","solve_d1_polyeq_equation"]]));
887 (prep_pbt thy "pbl_equ_univ_poly_deg2" [] e_pblID
888 (["degree_2","polynomial","univariate","equation"],
889 [("#Given" ,["equality e_e","solveFor v_v"]),
890 ("#Where" ,["matches (?a = 0) e_e",
891 "(lhs e_e) is_poly_in v_v ",
892 "((lhs e_e) has_degree_in v_v ) = 2"]),
893 ("#Find" ,["solutions v_v'i'"])
895 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
896 [["PolyEq","solve_d2_polyeq_equation"]]));
899 (prep_pbt thy "pbl_equ_univ_poly_deg2_sqonly" [] e_pblID
900 (["sq_only","degree_2","polynomial","univariate","equation"],
901 [("#Given" ,["equality e_e","solveFor v_v"]),
902 ("#Where" ,["matches ( ?a + ?v_^^^2 = 0) e_e | " ^
903 "matches ( ?a + ?b*?v_^^^2 = 0) e_e | " ^
904 "matches ( ?v_^^^2 = 0) e_e | " ^
905 "matches ( ?b*?v_^^^2 = 0) e_e" ,
906 "Not (matches (?a + ?v_ + ?v_^^^2 = 0) e_e) &" ^
907 "Not (matches (?a + ?b*?v_ + ?v_^^^2 = 0) e_e) &" ^
908 "Not (matches (?a + ?v_ + ?c*?v_^^^2 = 0) e_e) &" ^
909 "Not (matches (?a + ?b*?v_ + ?c*?v_^^^2 = 0) e_e) &" ^
910 "Not (matches ( ?v_ + ?v_^^^2 = 0) e_e) &" ^
911 "Not (matches ( ?b*?v_ + ?v_^^^2 = 0) e_e) &" ^
912 "Not (matches ( ?v_ + ?c*?v_^^^2 = 0) e_e) &" ^
913 "Not (matches ( ?b*?v_ + ?c*?v_^^^2 = 0) e_e)"]),
914 ("#Find" ,["solutions v_v'i'"])
916 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
917 [["PolyEq","solve_d2_polyeq_sqonly_equation"]]));
920 (prep_pbt thy "pbl_equ_univ_poly_deg2_bdvonly" [] e_pblID
921 (["bdv_only","degree_2","polynomial","univariate","equation"],
922 [("#Given" ,["equality e_e","solveFor v_v"]),
923 ("#Where" ,["matches (?a*?v_ + ?v_^^^2 = 0) e_e | " ^
924 "matches ( ?v_ + ?v_^^^2 = 0) e_e | " ^
925 "matches ( ?v_ + ?b*?v_^^^2 = 0) e_e | " ^
926 "matches (?a*?v_ + ?b*?v_^^^2 = 0) e_e | " ^
927 "matches ( ?v_^^^2 = 0) e_e | " ^
928 "matches ( ?b*?v_^^^2 = 0) e_e "]),
929 ("#Find" ,["solutions v_v'i'"])
931 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
932 [["PolyEq","solve_d2_polyeq_bdvonly_equation"]]));
935 (prep_pbt thy "pbl_equ_univ_poly_deg2_pq" [] e_pblID
936 (["pqFormula","degree_2","polynomial","univariate","equation"],
937 [("#Given" ,["equality e_e","solveFor v_v"]),
938 ("#Where" ,["matches (?a + 1*?v_^^^2 = 0) e_e | " ^
939 "matches (?a + ?v_^^^2 = 0) e_e"]),
940 ("#Find" ,["solutions v_v'i'"])
942 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
943 [["PolyEq","solve_d2_polyeq_pq_equation"]]));
946 (prep_pbt thy "pbl_equ_univ_poly_deg2_abc" [] e_pblID
947 (["abcFormula","degree_2","polynomial","univariate","equation"],
948 [("#Given" ,["equality e_e","solveFor v_v"]),
949 ("#Where" ,["matches (?a + ?v_^^^2 = 0) e_e | " ^
950 "matches (?a + ?b*?v_^^^2 = 0) e_e"]),
951 ("#Find" ,["solutions v_v'i'"])
953 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
954 [["PolyEq","solve_d2_polyeq_abc_equation"]]));
959 (prep_pbt thy "pbl_equ_univ_poly_deg3" [] e_pblID
960 (["degree_3","polynomial","univariate","equation"],
961 [("#Given" ,["equality e_e","solveFor v_v"]),
962 ("#Where" ,["matches (?a = 0) e_e",
963 "(lhs e_e) is_poly_in v_v ",
964 "((lhs e_e) has_degree_in v_v) = 3"]),
965 ("#Find" ,["solutions v_v'i'"])
967 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
968 [["PolyEq","solve_d3_polyeq_equation"]]));
972 (prep_pbt thy "pbl_equ_univ_poly_deg4" [] e_pblID
973 (["degree_4","polynomial","univariate","equation"],
974 [("#Given" ,["equality e_e","solveFor v_v"]),
975 ("#Where" ,["matches (?a = 0) e_e",
976 "(lhs e_e) is_poly_in v_v ",
977 "((lhs e_e) has_degree_in v_v) = 4"]),
978 ("#Find" ,["solutions v_v'i'"])
980 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
981 [(*["PolyEq","solve_d4_polyeq_equation"]*)]));
983 (*--- normalize ---*)
985 (prep_pbt thy "pbl_equ_univ_poly_norm" [] e_pblID
986 (["normalize","polynomial","univariate","equation"],
987 [("#Given" ,["equality e_e","solveFor v_v"]),
988 ("#Where" ,["(Not((matches (?a = 0 ) e_e ))) |" ^
989 "(Not(((lhs e_e) is_poly_in v_v)))"]),
990 ("#Find" ,["solutions v_v'i'"])
992 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
993 [["PolyEq","normalize_poly"]]));
994 (*-------------------------expanded-----------------------*)
996 (prep_pbt thy "pbl_equ_univ_expand" [] e_pblID
997 (["expanded","univariate","equation"],
998 [("#Given" ,["equality e_e","solveFor v_v"]),
999 ("#Where" ,["matches (?a = 0) e_e",
1000 "(lhs e_e) is_expanded_in v_v "]),
1001 ("#Find" ,["solutions v_v'i'"])
1003 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
1008 (prep_pbt thy "pbl_equ_univ_expand_deg2" [] e_pblID
1009 (["degree_2","expanded","univariate","equation"],
1010 [("#Given" ,["equality e_e","solveFor v_v"]),
1011 ("#Where" ,["((lhs e_e) has_degree_in v_v) = 2"]),
1012 ("#Find" ,["solutions v_v'i'"])
1014 PolyEq_prls, SOME "solve (e_e::bool, v_v)",
1015 [["PolyEq","complete_square"]]));
1020 "Script Normalize_poly (e_e::bool) (v_v::real) = " ^
1021 "(let e_e =((Try (Rewrite all_left False)) @@ " ^
1022 " (Try (Repeat (Rewrite makex1_x False))) @@ " ^
1023 " (Try (Repeat (Rewrite_Set expand_binoms False))) @@ " ^
1024 " (Try (Repeat (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1025 " make_ratpoly_in False))) @@ " ^
1026 " (Try (Repeat (Rewrite_Set polyeq_simplify False)))) e_e " ^
1027 " in (SubProblem (PolyEq',[polynomial,univariate,equation], [no_met]) " ^
1028 " [BOOL e_e, REAL v_v]))";
1032 "-------------------------methods-----------------------";
1034 (prep_met thy "met_polyeq" [] e_metID
1037 {rew_ord'="tless_true",rls'=Atools_erls,calc = [], srls = e_rls, prls=e_rls,
1038 crls=PolyEq_crls, nrls=norm_Rational}, "empty_script"));
1041 (prep_met thy "met_polyeq_norm" [] e_metID
1042 (["PolyEq","normalize_poly"],
1043 [("#Given" ,["equality e_e","solveFor v_v"]),
1044 ("#Where" ,["(Not((matches (?a = 0 ) e_e ))) |" ^
1045 "(Not(((lhs e_e) is_poly_in v_v)))"]),
1046 ("#Find" ,["solutions v_v'i'"])
1048 {rew_ord'="termlessI",
1053 crls=PolyEq_crls, nrls=norm_Rational},
1054 "Script Normalize_poly (e_e::bool) (v_v::real) = " ^
1055 "(let e_e =((Try (Rewrite all_left False)) @@ " ^
1056 " (Try (Repeat (Rewrite makex1_x False))) @@ " ^
1057 " (Try (Repeat (Rewrite_Set expand_binoms False))) @@ " ^
1058 " (Try (Repeat (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1059 " make_ratpoly_in False))) @@ " ^
1060 " (Try (Repeat (Rewrite_Set polyeq_simplify False)))) e_e " ^
1061 " in (SubProblem (PolyEq',[polynomial,univariate,equation], [no_met]) " ^
1062 " [BOOL e_e, REAL v_v]))"
1068 (prep_met thy "met_polyeq_d0" [] e_metID
1069 (["PolyEq","solve_d0_polyeq_equation"],
1070 [("#Given" ,["equality e_e","solveFor v_v"]),
1071 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1072 "((lhs e_e) has_degree_in v_v) = 0"]),
1073 ("#Find" ,["solutions v_v'i'"])
1075 {rew_ord'="termlessI",
1079 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1080 crls=PolyEq_crls, nrls=norm_Rational},
1081 "Script Solve_d0_polyeq_equation (e_e::bool) (v_v::real) = " ^
1082 "(let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1083 " d0_polyeq_simplify False))) e_e " ^
1084 " in ((Or_to_List e_e)::bool list))"
1089 (prep_met thy "met_polyeq_d1" [] e_metID
1090 (["PolyEq","solve_d1_polyeq_equation"],
1091 [("#Given" ,["equality e_e","solveFor v_v"]),
1092 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1093 "((lhs e_e) has_degree_in v_v) = 1"]),
1094 ("#Find" ,["solutions v_v'i'"])
1096 {rew_ord'="termlessI", rls'=PolyEq_erls, srls=e_rls, prls=PolyEq_prls,
1097 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1098 crls=PolyEq_crls, nrls=norm_Rational},
1099 "Script Solve_d1_polyeq_equation (e_e::bool) (v_v::real) = " ^
1100 "(let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1101 " d1_polyeq_simplify True)) @@ " ^
1102 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1103 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1104 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1105 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1110 (prep_met thy "met_polyeq_d22" [] e_metID
1111 (["PolyEq","solve_d2_polyeq_equation"],
1112 [("#Given" ,["equality e_e","solveFor v_v"]),
1113 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1114 "((lhs e_e) has_degree_in v_v) = 2"]),
1115 ("#Find" ,["solutions v_v'i'"])
1117 {rew_ord'="termlessI",
1121 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1122 crls=PolyEq_crls, nrls=norm_Rational},
1123 "Script Solve_d2_polyeq_equation (e_e::bool) (v_v::real) = " ^
1124 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1125 " d2_polyeq_simplify True)) @@ " ^
1126 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1127 " (Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1128 " d1_polyeq_simplify True)) @@ " ^
1129 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1130 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1131 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1132 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1137 (prep_met thy "met_polyeq_d2_bdvonly" [] e_metID
1138 (["PolyEq","solve_d2_polyeq_bdvonly_equation"],
1139 [("#Given" ,["equality e_e","solveFor v_v"]),
1140 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1141 "((lhs e_e) has_degree_in v_v) = 2"]),
1142 ("#Find" ,["solutions v_v'i'"])
1144 {rew_ord'="termlessI",
1148 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1149 crls=PolyEq_crls, nrls=norm_Rational},
1150 "Script Solve_d2_polyeq_bdvonly_equation (e_e::bool) (v_v::real) =" ^
1151 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1152 " d2_polyeq_bdv_only_simplify True)) @@ " ^
1153 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1154 " (Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1155 " d1_polyeq_simplify True)) @@ " ^
1156 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1157 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1158 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1159 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1164 (prep_met thy "met_polyeq_d2_sqonly" [] e_metID
1165 (["PolyEq","solve_d2_polyeq_sqonly_equation"],
1166 [("#Given" ,["equality e_e","solveFor v_v"]),
1167 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1168 "((lhs e_e) has_degree_in v_v) = 2"]),
1169 ("#Find" ,["solutions v_v'i'"])
1171 {rew_ord'="termlessI",
1175 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1176 crls=PolyEq_crls, nrls=norm_Rational},
1177 "Script Solve_d2_polyeq_sqonly_equation (e_e::bool) (v_v::real) =" ^
1178 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1179 " d2_polyeq_sq_only_simplify True)) @@ " ^
1180 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1181 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e; " ^
1182 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1183 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1188 (prep_met thy "met_polyeq_d2_pq" [] e_metID
1189 (["PolyEq","solve_d2_polyeq_pq_equation"],
1190 [("#Given" ,["equality e_e","solveFor v_v"]),
1191 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1192 "((lhs e_e) has_degree_in v_v) = 2"]),
1193 ("#Find" ,["solutions v_v'i'"])
1195 {rew_ord'="termlessI",
1199 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1200 crls=PolyEq_crls, nrls=norm_Rational},
1201 "Script Solve_d2_polyeq_pq_equation (e_e::bool) (v_v::real) = " ^
1202 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1203 " d2_polyeq_pqFormula_simplify True)) @@ " ^
1204 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1205 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1206 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1207 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1212 (prep_met thy "met_polyeq_d2_abc" [] e_metID
1213 (["PolyEq","solve_d2_polyeq_abc_equation"],
1214 [("#Given" ,["equality e_e","solveFor v_v"]),
1215 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1216 "((lhs e_e) has_degree_in v_v) = 2"]),
1217 ("#Find" ,["solutions v_v'i'"])
1219 {rew_ord'="termlessI",
1223 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1224 crls=PolyEq_crls, nrls=norm_Rational},
1225 "Script Solve_d2_polyeq_abc_equation (e_e::bool) (v_v::real) = " ^
1226 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1227 " d2_polyeq_abcFormula_simplify True)) @@ " ^
1228 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1229 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1230 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1231 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1236 (prep_met thy "met_polyeq_d3" [] e_metID
1237 (["PolyEq","solve_d3_polyeq_equation"],
1238 [("#Given" ,["equality e_e","solveFor v_v"]),
1239 ("#Where" ,["(lhs e_e) is_poly_in v_v ",
1240 "((lhs e_e) has_degree_in v_v) = 3"]),
1241 ("#Find" ,["solutions v_v'i'"])
1243 {rew_ord'="termlessI",
1247 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1248 crls=PolyEq_crls, nrls=norm_Rational},
1249 "Script Solve_d3_polyeq_equation (e_e::bool) (v_v::real) = " ^
1250 " (let e_e = ((Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1251 " d3_polyeq_simplify True)) @@ " ^
1252 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1253 " (Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1254 " d2_polyeq_simplify True)) @@ " ^
1255 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1256 " (Try (Rewrite_Set_Inst [(bdv,v_v::real)] " ^
1257 " d1_polyeq_simplify True)) @@ " ^
1258 " (Try (Rewrite_Set polyeq_simplify False)) @@ " ^
1259 " (Try (Rewrite_Set norm_Rational_parenthesized False))) e_e;" ^
1260 " (L_L::bool list) = ((Or_to_List e_e)::bool list) " ^
1261 " in Check_elementwise L_LL {(v_v::real). Assumptions} )"
1265 (*.solves all expanded (ie. normalized) terms of degree 2.*)
1266 (*Oct.02 restriction: 'eval_true 0 =< discriminant' ony for integer values
1267 by 'PolyEq_erls'; restricted until Float.thy is implemented*)
1269 (prep_met thy "met_polyeq_complsq" [] e_metID
1270 (["PolyEq","complete_square"],
1271 [("#Given" ,["equality e_e","solveFor v_v"]),
1272 ("#Where" ,["matches (?a = 0) e_e",
1273 "((lhs e_e) has_degree_in v_v) = 2"]),
1274 ("#Find" ,["solutions v_v'i'"])
1276 {rew_ord'="termlessI",rls'=PolyEq_erls,srls=e_rls,prls=PolyEq_prls,
1277 calc=[("sqrt", ("NthRoot.sqrt", eval_sqrt "#sqrt_"))],
1278 crls=PolyEq_crls, nrls=norm_Rational},
1279 "Script Complete_square (e_e::bool) (v_v::real) = " ^
1281 " ((Try (Rewrite_Set_Inst [(bdv,v_v)] cancel_leading_coeff True)) " ^
1282 " @@ (Try (Rewrite_Set_Inst [(bdv,v_v)] complete_square True)) " ^
1283 " @@ (Try (Rewrite square_explicit1 False)) " ^
1284 " @@ (Try (Rewrite square_explicit2 False)) " ^
1285 " @@ (Rewrite root_plus_minus True) " ^
1286 " @@ (Try (Repeat (Rewrite_Inst [(bdv,v_v)] bdv_explicit1 False))) " ^
1287 " @@ (Try (Repeat (Rewrite_Inst [(bdv,v_v)] bdv_explicit2 False))) " ^
1288 " @@ (Try (Repeat " ^
1289 " (Rewrite_Inst [(bdv,v_v)] bdv_explicit3 False))) " ^
1290 " @@ (Try (Rewrite_Set calculate_RootRat False)) " ^
1291 " @@ (Try (Repeat (Calculate SQRT)))) e_e " ^
1292 " in ((Or_to_List e_e)::bool list))"
1297 (* termorder hacked by MG *)
1298 local (*. for make_polynomial_in .*)
1300 open Term; (* for type order = EQUAL | LESS | GREATER *)
1302 fun pr_ord EQUAL = "EQUAL"
1303 | pr_ord LESS = "LESS"
1304 | pr_ord GREATER = "GREATER";
1306 fun dest_hd' x (Const (a, T)) = (((a, 0), T), 0)
1307 | dest_hd' x (t as Free (a, T)) =
1308 if x = t then ((("|||||||||||||", 0), T), 0) (*WN*)
1309 else (((a, 0), T), 1)
1310 | dest_hd' x (Var v) = (v, 2)
1311 | dest_hd' x (Bound i) = ((("", i), dummyT), 3)
1312 | dest_hd' x (Abs (_, T, _)) = ((("", 0), T), 4);
1314 fun size_of_term' x (Const ("Atools.pow",_) $ Free (var,_) $ Free (pot,_)) =
1317 (if xstr = var then 1000*(the (int_of_str pot)) else 3)
1318 | _ => raise error ("size_of_term' called with subst = "^
1320 | size_of_term' x (Free (subst,_)) =
1322 (Free (xstr,_)) => (if xstr = subst then 1000 else 1)
1323 | _ => raise error ("size_of_term' called with subst = "^
1325 | size_of_term' x (Abs (_,_,body)) = 1 + size_of_term' x body
1326 | size_of_term' x (f$t) = size_of_term' x f + size_of_term' x t
1327 | size_of_term' x _ = 1;
1330 fun term_ord' x pr thy (Abs (_, T, t), Abs(_, U, u)) = (* ~ term.ML *)
1331 (case term_ord' x pr thy (t, u) of EQUAL => Term_Ord.typ_ord (T, U) | ord => ord)
1332 | term_ord' x pr thy (t, u) =
1335 val (f, ts) = strip_comb t and (g, us) = strip_comb u;
1336 val _=writeln("t= f@ts= \""^
1337 ((Syntax.string_of_term (thy2ctxt thy)) f)^"\" @ \"["^
1338 (commas(map (Syntax.string_of_term (thy2ctxt thy)) ts))^"]\"");
1339 val _=writeln("u= g@us= \""^
1340 ((Syntax.string_of_term (thy2ctxt thy)) g)^"\" @ \"["^
1341 (commas(map (Syntax.string_of_term (thy2ctxt thy)) us))^"]\"");
1342 val _=writeln("size_of_term(t,u)= ("^
1343 (string_of_int(size_of_term' x t))^", "^
1344 (string_of_int(size_of_term' x u))^")");
1345 val _=writeln("hd_ord(f,g) = "^((pr_ord o (hd_ord x))(f,g)));
1346 val _=writeln("terms_ord(ts,us) = "^
1347 ((pr_ord o (terms_ord x) str false)(ts, us)));
1348 val _=writeln("-------");
1351 case int_ord (size_of_term' x t, size_of_term' x u) of
1353 let val (f, ts) = strip_comb t and (g, us) = strip_comb u in
1354 (case hd_ord x (f, g) of EQUAL => (terms_ord x str pr) (ts, us)
1358 and hd_ord x (f, g) = (* ~ term.ML *)
1359 prod_ord (prod_ord Term_Ord.indexname_ord Term_Ord.typ_ord)
1360 int_ord (dest_hd' x f, dest_hd' x g)
1361 and terms_ord x str pr (ts, us) =
1362 list_ord (term_ord' x pr (assoc_thy "Isac"))(ts, us);
1365 fun ord_make_polynomial_in (pr:bool) thy subst tu =
1367 (* val _=writeln("*** subs variable is: "^(subst2str subst)); *)
1370 (_,x)::_ => (term_ord' x pr thy tu = LESS)
1371 | _ => raise error ("ord_make_polynomial_in called with subst = "^
1378 val order_add_mult_in = prep_rls(
1379 Rls{id = "order_add_mult_in", preconds = [],
1380 rew_ord = ("ord_make_polynomial_in",
1381 ord_make_polynomial_in false (theory "Poly")),
1382 erls = e_rls,srls = Erls,
1385 rules = [Thm ("real_mult_commute",num_str @{thm real_mult_commute}),
1387 Thm ("real_mult_left_commute",num_str @{thm real_mult_left_commute}),
1388 (*z1.0 * (z2.0 * z3.0) = z2.0 * (z1.0 * z3.0)*)
1389 Thm ("real_mult_assoc",num_str @{thm real_mult_assoc}),
1390 (*z1.0 * z2.0 * z3.0 = z1.0 * (z2.0 * z3.0)*)
1391 Thm ("add_commute",num_str @{thm add_commute}),
1393 Thm ("add_left_commute",num_str @{thm add_left_commute}),
1394 (*x + (y + z) = y + (x + z)*)
1395 Thm ("add_assoc",num_str @{thm add_assoc})
1396 (*z1.0 + z2.0 + z3.0 = z1.0 + (z2.0 + z3.0)*)
1397 ], scr = EmptyScr}:rls);
1401 val collect_bdv = prep_rls(
1402 Rls{id = "collect_bdv", preconds = [],
1403 rew_ord = ("dummy_ord", dummy_ord),
1404 erls = e_rls,srls = Erls,
1407 rules = [Thm ("bdv_collect_1",num_str @{thm bdv_collect_1}),
1408 Thm ("bdv_collect_2",num_str @{thm bdv_collect_2}),
1409 Thm ("bdv_collect_3",num_str @{thm bdv_collect_3}),
1411 Thm ("bdv_collect_assoc1_1",num_str @{thm bdv_collect_assoc1_1}),
1412 Thm ("bdv_collect_assoc1_2",num_str @{thm bdv_collect_assoc1_2}),
1413 Thm ("bdv_collect_assoc1_3",num_str @{thm bdv_collect_assoc1_3}),
1415 Thm ("bdv_collect_assoc2_1",num_str @{thm bdv_collect_assoc2_1}),
1416 Thm ("bdv_collect_assoc2_2",num_str @{thm bdv_collect_assoc2_2}),
1417 Thm ("bdv_collect_assoc2_3",num_str @{thm bdv_collect_assoc2_3}),
1420 Thm ("bdv_n_collect_1",num_str @{thm bdv_n_collect_1}),
1421 Thm ("bdv_n_collect_2",num_str @{thm bdv_n_collect_2}),
1422 Thm ("bdv_n_collect_3",num_str @{thm bdv_n_collect_3}),
1424 Thm ("bdv_n_collect_assoc1_1",num_str @{thm bdv_n_collect_assoc1_1}),
1425 Thm ("bdv_n_collect_assoc1_2",num_str @{thm bdv_n_collect_assoc1_2}),
1426 Thm ("bdv_n_collect_assoc1_3",num_str @{thm bdv_n_collect_assoc1_3}),
1428 Thm ("bdv_n_collect_assoc2_1",num_str @{thm bdv_n_collect_assoc2_1}),
1429 Thm ("bdv_n_collect_assoc2_2",num_str @{thm bdv_n_collect_assoc2_2}),
1430 Thm ("bdv_n_collect_assoc2_3",num_str @{thm bdv_n_collect_assoc2_3})
1431 ], scr = EmptyScr}:rls);
1435 (*.transforms an arbitrary term without roots to a polynomial [4]
1436 according to knowledge/Poly.sml.*)
1437 val make_polynomial_in = prep_rls(
1438 Seq {id = "make_polynomial_in", preconds = []:term list,
1439 rew_ord = ("dummy_ord", dummy_ord),
1440 erls = Atools_erls, srls = Erls,
1441 calc = [], (*asm_thm = [],*)
1442 rules = [Rls_ expand_poly,
1443 Rls_ order_add_mult_in,
1444 Rls_ simplify_power,
1445 Rls_ collect_numerals,
1447 Thm ("realpow_oneI",num_str @{thm realpow_oneI}),
1448 Rls_ discard_parentheses,
1457 append_rls "separate_bdvs"
1459 [Thm ("separate_bdv", num_str @{thm separate_bdv}),
1460 (*"?a * ?bdv / ?b = ?a / ?b * ?bdv"*)
1461 Thm ("separate_bdv_n", num_str @{thm separate_bdv_n}),
1462 Thm ("separate_1_bdv", num_str @{thm separate_1_bdv}),
1463 (*"?bdv / ?b = (1 / ?b) * ?bdv"*)
1464 Thm ("separate_1_bdv_n", num_str @{thm separate_1_bdv_n}),
1465 (*"?bdv ^^^ ?n / ?b = 1 / ?b * ?bdv ^^^ ?n"*)
1466 Thm ("add_divide_distrib",
1467 num_str @{thm add_divide_distrib})
1468 (*"(?x + ?y) / ?z = ?x / ?z + ?y / ?z"
1469 WN051031 DOES NOT BELONG TO HERE*)
1473 val make_ratpoly_in = prep_rls(
1474 Seq {id = "make_ratpoly_in", preconds = []:term list,
1475 rew_ord = ("dummy_ord", dummy_ord),
1476 erls = Atools_erls, srls = Erls,
1477 calc = [], (*asm_thm = [],*)
1478 rules = [Rls_ norm_Rational,
1479 Rls_ order_add_mult_in,
1480 Rls_ discard_parentheses,
1482 (* Rls_ rearrange_assoc, WN060916 why does cancel_p not work?*)
1484 (*Calc ("Rings.inverse_class.divide" ,eval_cancel "#divide_e") too weak!*)
1486 scr = EmptyScr}:rls);
1489 ruleset' := overwritelthy @{theory} (!ruleset',
1490 [("order_add_mult_in", order_add_mult_in),
1491 ("collect_bdv", collect_bdv),
1492 ("make_polynomial_in", make_polynomial_in),
1493 ("make_ratpoly_in", make_ratpoly_in),
1494 ("separate_bdvs", separate_bdvs)